TITLE by Rodrigo P Maruyama

Table of contents

  1. Initial Setup

  1. Introduction

  2. Data Structure:
  1. Univariate Plots Section
  1. Bivariate Plots Section
  1. Multivariate Plots Section
  1. Machine Learning
  1. Final Plots and Summary

  1. Reflection

  2. Resources

Initial Setup

Working directory

setwd("D://Documents/ead/Udacity/dsNanodegree/dataAnalysisR/project/")

Package Instalation

install.packages('kable')
install.packages("markdown", dependencies = TRUE)
install.packages("knitr", dependencies = TRUE)
install.packages("ggplot2", dependencies = TRUE)
install.packages("knitr", dependencies = TRUE)
install.packages("dplyr", dependencies = TRUE)
install.packages('GGally', dependencies = TRUE)
install.packages('tidyverse', dependencies = TRUE)
install.packages('ggthemes', dependencies = TRUE)
install.packages('corrplot', dependencies = TRUE)
install.packages('ggbiplot2', dependencies = TRUE)
install.packages('e1071', dependencies = TRUE)
install.packages('rpart', dependencies = TRUE)
install.packages('randomForest', dependencies = TRUE)
install.packages('ggfortify', dependencies = TRUE)
install.packages('ROCR', dependencies = TRUE)

Libraries

library(ROCR)
library(ggfortify)
library(ggplot2)
library(knitr)
library(dplyr)
library(GGally)
library(tidyverse)
library(ggthemes)
library(gridExtra)
library(corrplot)
library(grid)
library(lattice)
library(e1071)
library(rpart)
library(randomForest)
library(knitr) 
library(markdown)
library(htmlTable)

Loading Dataset

# Load the Data
wdf <- read.csv('data/wineQualityWhites.csv')
wdf$X <- NULL

Introduction

We will study a white wine dataset with 4898 observations and 12 features. One of then is the quality of the wine from 0 to 10, and the others are chemical information. You can find a summary regarding the features in the table below.

Dataset link: here
Article link: here

The Dataset Structure

Dataset size

dim(wdf)
## [1] 4898   12

Summary of the Dataset:

swdf <- summary(wdf)
swdf <- t.data.frame(swdf)
write.csv(swdf, file = 'summary.csv')
Feature unit Min 1st Qu. Median Mean 3rd Qu. Max
fixed.acidity [g(tartaric acid)/dm^3] 3.80 6.30 6.80 6.86 7.30 14.20
volatile.acidity [g(acetic acid)/dm^3] 0.08 0.21 0.26 0.28 0.32 1.10
citric.acid [g/dm^3] 0.00 0.27 0.32 0.33 0.39 1.66
residual.sugar [g/dm^3] 0.60 1.70 5.20 6.39 9.90 65.80
chlorides [g(acetic acid)/dm^3] 0.01 0.04 0.04 0.05 0.05 0.35
free.sulfur.dioxide [mg/dm^3] 2.00 23.00 34.00 35.31 46.00 289.00
total.sulfur.dioxide [g/cm^3] 9.00 108.00 134.00 138.40 167.00 440.00
density [g/cm^3] 0.99 0.99 0.99 0.99 1.00 1.04
pH 2.72 3.09 3.18 3.19 3.28 3.82
sulphates [g(potassium sulphate)/dm^3] 0.22 0.41 0.47 0.49 0.55 1.08
alcohol [% vol.] 8.00 9.50 10.40 10.51 11.40 14.20
quality 3.00 5.00 6.00 5.88 6.00 9.00

Univariate Plots Section

Histogram for each feature

p1 <- ggplot(aes(x=fixed.acidity), data = wdf) +
  geom_bar(fill='#99CCFF')
p2 <- ggplot(aes(x=volatile.acidity), data = wdf) +
  geom_bar(fill='#99CCFF')
p3 <- ggplot(aes(x=citric.acid), data = wdf) +
  geom_bar(fill='#99CCFF')
p4 <- ggplot(aes(x=residual.sugar), data = wdf) +
  geom_bar(fill='#99CCFF')
p5 <- ggplot(aes(x=chlorides), data = wdf) +
  geom_bar(fill='#99CCFF')
p6 <- ggplot(aes(x=free.sulfur.dioxide), data = wdf) +
  geom_bar(fill='#99CCFF')
p7 <- ggplot(aes(x=total.sulfur.dioxide), data = wdf) +
  geom_bar(fill='#99CCFF')
p8 <- ggplot(aes(x=density), data = wdf) +
  geom_bar(fill='#99CCFF')
p9 <- ggplot(aes(x=pH), data = wdf) +
  geom_bar(fill='#99CCFF')
p10 <- ggplot(aes(x=sulphates), data = wdf) +
  geom_bar(fill='#99CCFF')
p11 <- ggplot(aes(x=alcohol), data = wdf) +
  geom_bar(fill='#99CCFF')
p12 <- ggplot(aes(x=quality), data = wdf) +
  geom_bar(fill='#99CCFF')

u1 <- grid.arrange(p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, ncol = 4, top = textGrob("Histograms for all features",gp=gpar(fontsize=15,font=3)))

ggsave(file = 'pictures/1_univariate.png', u1)
Histogram

Histogram

Histogram for all features in the dataset. We can observe that most of the graphic have a normal distribution with a tendency for a positive skeew. The next section we will remove the outliers based on our observation on the plots below and re-plot the Histograms again.

Removing Outliers

wdf.outliers <- data.frame(wdf)

wdf.outliers <- subset(wdf.outliers, wdf.outliers$fixed.acidity < 11)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$volatile.acidity < 0.75)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$citric.acid < 1)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$residual.sugar < 30)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$chlorides < 0.10)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$free.sulfur.dioxide < 125)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$total.sulfur.dioxide < 350)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$density < 1.005)

Histogram without outliers

Histogram without outliers

Histogram without outliers

Histograms re-ploted without outliers.

Density plot for each feature with stat lines

# Using a for loop for better programming practice and to save lines of code :)

feature.list <- names(wdf)
p <- list()
a <- 0
for (var in feature.list) {
  a <- a + 1

  p[[a]] <- ggplot(data = wdf, aes_string(x=var)) +
    geom_density(fill='#99CCFF') +
    geom_vline(aes_string(xintercept=mean(wdf[, var])),
               color='blue', size=0.5) +
    geom_vline(aes_string(xintercept=median(wdf[, var])),
               color='red', size=0.5) +
    geom_vline(aes_string(xintercept=quantile(wdf[, var], 0.25)),
               linetype='dashed', size=0.5) +
    geom_vline(aes_string(xintercept=quantile(wdf[, var], 0.75)),
               linetype='dashed', size=0.5) +
    ylab(NULL)

}

ggsave(file = 'pictures/density_univariate_outliers.png', do.call(grid.arrange, p))

Density plots for each feature with stats lines

univariate density plots without outliers

univariate density plots without outliers

In this plot and from the histograms above we can see the mean, median, 1st quantile and 3rd quantile over each density distribution and a very normal distribution for all features except for residual.sugar that have a very slightly positve skeew.

Quality.2 feature creation

# | classification | Criterion       |
# |----------------|-----------------|
# | Bad            | quality < 6     |
# | Normal         | quality = 6     |
# | Good           | quality > 6     |


wdf$quality.2 <- ifelse(wdf$quality < 6, 'bad', ifelse(wdf$quality == 6, 'normal', 'good'))
wdf$quality.2 <- as.factor(wdf$quality.2)

table(wdf$quality.2)
## 
##    bad   good normal 
##   1640   1060   2198
wdf$quality.2 <- NULL
Quality.2 raw dataset outliers removed dataset
bad 1640 1565
good 1060 1055
normal 2198 2139 
# Pie plot creation with percent legend

rating = as.numeric(c(1565, 2139, 1055))
percent <- round(100*rating/sum(rating), 1)
colors = c("red", "orange", "blue")
lable <- c('Bad', 'Normal', 'Good')
pie(rating, labels = lable, main = 'Wine quality Pie chart distribution', col = colors)
Pie chart

Pie chart

Univariate Analysis

What is the structure of your dataset?

See Dataset Structure above.

What is/are the main feature(s) of interest in your dataset?

The quality is the main feature of interest.

What other features in the dataset do you think will help support your investigation into your feature(s) of interest?

From Wine specialists the basics characteristics are:

  1. Sweetness
  2. Acidity
  3. Tannin
  4. Alcohol
  5. Body

Tannin is correlated with phenolic compounds however we don’t have this variable in our dataset, and Body is a mix from all characteristics mentioned above. Then, I will focusing on the following variables:

  1. quality
  2. pH
  3. residual.sugar
  4. alcohol

Did you create any new variables from existing variables in the dataset?

Yes, I created a new variable called quality.2 from quality as in the table below:

classification Criterion
Bad quality < 6
Normal quality = 6
Good quality > 6

Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?

No. I didn’t change the original data.

Bivariate Plots Section

GGPAIRS plot

ggpairs(wdf, title = 'GGPAIRS') + 
  theme(panel.grid.minor = element_blank(), panel.grid.major = element_blank(),         
  axis.line=element_blank(), axis.text=element_blank())
Ggpairs

Ggpairs

CORRPLOT

cor.wdf <- cor(wdf)
corrplot.mixed(cor.wdf, tl.pos = 'lt', mar=c(2,0,2,0), title = 'Corrplot graphic')
Corrplot

Corrplot

Looking at the “ggpairs” and “corrplot” plots result it is easy to have a good idea about the correlations between the features. In the table below there is a list with a few pairs with a positive, negative and zero correlation. The positive correlation have 4 rows but we will discharge the number 2 because those features have similar properties.

Positive, Negative and Zero Correlation Table

Positive correlation correlation correlation outliers
1 density x residual.sugar 0.84 0.84
2 total.sulfur.dioxide x free.sulfur.dioxide 0.62 0.61
3 density x total.sulfur.dioxide 0.53 0.55
4 quality x alcohol 0.44 0.44
Negative correlation correlation correlation outliers
1 density x alcohol -0.78 -0.81
2 total.sulfur.dioxide x alcohol -0.45 -0.46
3 alcohol x residual.sugar -0.45 -0.48
Zero correlation correlation correlation outliers
1 quality x citric.acid ~ 0 ~ 0
2 sulphates x chlorides ~ 0 0.06
3 density x volatily.acidity ~ 0 -0.03

Bivariate Boxplots

# Removing outliers for density and residual.sugar for better visualization

# Positive correlation plots
p1 <- ggplot(data = wdf, aes(x = density, y = residual.sugar)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  scale_y_continuous(limits = c(0, 25)) +
  ggtitle('density X residual.sugar')

p2 <- ggplot(data = wdf, aes(x = density, y = total.sulfur.dioxide)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  ggtitle('density X total.sulfur.dioxide')

p3 <- ggplot(data = wdf, aes(x = quality, y = alcohol)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  ggtitle('quality X alcohol')

# Negative correlation plots
p4 <- ggplot(data = wdf, aes(x = density, y = alcohol)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  ggtitle('density X alcohol')

p5 <- ggplot(data = wdf, aes(y = total.sulfur.dioxide, x = alcohol)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  ggtitle('total.sulfur.dioxide X alcohol')

p6 <- ggplot(data = wdf, aes(x = alcohol, y = residual.sugar)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  scale_y_continuous(limits = c(0, 30)) +
  ggtitle('alcohol X residual.sugar')

# Zero correlation
p7 <- ggplot(data = wdf, aes(x = quality, y = citric.acid)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  scale_y_continuous(limits = c(0, 1)) +
  ggtitle('quality X citric.acid')

p8 <- ggplot(data = wdf, aes(y = sulphates, x = chlorides)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  ggtitle('sulphates X chlorides')

p9 <- ggplot(data = wdf, aes(x = density, y = volatile.acidity)) +
  geom_boxplot(aes(group = cut_width(quality, 1)), fill = '#99CCFF') +
  scale_y_continuous(limits = c(0, 0.9)) +
  ggtitle('density X volatile.acidity')

grid1 <- grid.arrange(p1, p2, p3, ncol = 3, top = textGrob("Bivariate Boxplots with Positive Correlation",gp=gpar(fontsize=15,font=3)))

grid2 <- grid.arrange(p4, p5, p6, ncol = 3, top = textGrob("Bivariate Boxplots with Negative Correlation",gp=gpar(fontsize=15,font=3)))

grid3 <- grid.arrange(p7, p8, p9, ncol = 3, top = textGrob("Bivariate Boxplots with Zero Correlation",gp=gpar(fontsize=15,font=3)))

ggsave(file = 'pictures/1_boxplot_bivariate_outliers.png', grid1)
ggsave(file = 'pictures/2_boxplot_bivariate_outliers.png', grid2)
ggsave(file = 'pictures/3_boxplot_bivariate_outliers.png', grid3)
Bivariate Boxplots

Bivariate Boxplots

Bivariate Boxplots

Bivariate Boxplots

Bivariate Boxplots

Bivariate Boxplots

Bivariate Scatter plots with linear regression line

# Removing outliers for better visualization

# Solution for Warning message: "Continuous x aesthetic -- did you forget aes(group=...)? "
# https://ggplot2.tidyverse.org/reference/geom_boxplot.html

# Positive correlation plots
p1 <- ggplot(data = wdf, aes(x = density, y = residual.sugar)) +
  geom_point() +
  geom_smooth(method='lm',formula=y~x) +
  scale_x_continuous(limits = c(0.98, 1.01)) +
  scale_y_continuous(limits = c(0, 30))

p2 <- ggplot(data = wdf, aes(x = density, y = total.sulfur.dioxide)) +
  geom_point() +
  geom_smooth(method='lm',formula=y~x) +
  scale_x_continuous(limits = c(0.98, 1.01))

p3 <- ggplot(data = wdf, aes(x = quality, y = alcohol)) +
  geom_point()

# Negative correlation plots
p4 <- ggplot(data = wdf, aes(x = density, y = alcohol)) +
  geom_point() +
  geom_smooth(method='lm',formula=y~x) +
  scale_x_continuous(limits = c(0.98, 1.01))

p5 <- ggplot(data = wdf, aes(y = total.sulfur.dioxide, x = alcohol)) +
  geom_point() +
  geom_smooth(method='lm',formula=y~x)

p6 <- ggplot(data = wdf, aes(x = alcohol, y = residual.sugar)) +
  geom_point() +
  geom_smooth(method='lm',formula=y~x) +
  scale_y_continuous(limits = c(0, 30))

# Zero correlation
p7 <- ggplot(data = wdf, aes(x = quality, y = citric.acid)) +
  geom_point()

p8 <- ggplot(data = wdf, aes(y = sulphates, x = chlorides)) +
  geom_point() +
  geom_smooth(method='lm',formula=y~x) +
  scale_x_continuous(limits = c(0, 0.2))

p9 <- ggplot(data = wdf, aes(x = density, y = volatile.acidity)) +
  geom_point() +
  geom_smooth(method='lm',formula=y~x) +
  scale_y_continuous(limits = c(0, 0.9)) +
  scale_x_continuous(limits = c(0.98, 1.01))

grid1 <- grid.arrange(p1, p2, p3, ncol = 3, top = textGrob("Bivariate Scatter plot with Positive Correlation",gp=gpar(fontsize=15,font=3)))

grid2 <- grid.arrange(p4, p5, p6, ncol = 3, top = textGrob("Bivariate Scatter plot with Negative Correlation",gp=gpar(fontsize=15,font=3)))

grid3 <- grid.arrange(p7, p8, p9, ncol = 3, top = textGrob("Bivariate Scatter plot with Zero Correlation",gp=gpar(fontsize=15,font=3)))

ggsave(file = 'pictures/1_scatterplot_bivariate_outliers.png', grid1)
ggsave(file = 'pictures/2_scatterplot_bivariate_outliers.png', grid2)
ggsave(file = 'pictures/3_scatterplot_bivariate_outliers.png', grid3)
Positive COrrelation Bivariate Scatterplot

Positive COrrelation Bivariate Scatterplot

Negative Correlation Bivariate Scatterplot

Negative Correlation Bivariate Scatterplot

Zero Correlation Bivariate Scatterplot

Zero Correlation Bivariate Scatterplot

Bivariate Analysis

Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?

  • Strong Positive correlation

In the density_X_residual.sugar plot we can observe a strong correlation. The amount of wines with lower density and residual.sugar is bigger than high values. In density_X_total.sulfur.dioxide the plot have a eclipse format where the amount of wines have a concentration in the midle for both features but fot total.sulfur.dioxide they are spread much more.

  • Strong Negative correlation

In the density_X_alcohol plot we can see the expected behaivour once the alcohol density is lower than the water density. For both second and third plots they have a negative tendency nad for alcohol_X_residual.sugar they are a concentration of wines with lower residual.sugar quantities.

  • Zero Correlation

Those plots we can check what was expected from the correlation value. They don’t have any strong tendency.

Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?

No.

What was the strongest relationship you found?

Positive correlation correlation correlation outliers
1 density x residual.sugar 0.84 0.84
2 total.sulfur.dioxide x free.sulfur.dioxide 0.62 0.61
3 density x total.sulfur.dioxide 0.53 0.55
4 quality x alcohol 0.44 0.44

In this table we can see the correlation using a raw dataset and the dataset without oultliers we can’t see difference between them. We can disconsidering total.sulfur.dioxide x free.sulfur.dioxide beacuse one is part of the others.

Multivariate Plots Section

Highest Correlated features plots

# Multivariate plots with Linear Regression

p1 <- ggplot(data = wdf, aes(x = density, y = residual.sugar, colour = quality)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method='lm',formula=y~x) +
  scale_colour_gradientn(colours=rainbow(10)) +
  ggtitle('density X residual.sugar X quality')

p2 <- ggplot(data = wdf, aes(x = density, y = alcohol, colour = quality)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method='lm',formula=y~x) +
  scale_colour_gradientn(colours=rainbow(10)) +
  ggtitle('density X alcohol X quality')

p3 <- ggplot(data = wdf, aes(y = sulphates, x = chlorides, colour = quality)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method='lm',formula=y~x) +
  scale_colour_gradientn(colours=rainbow(10)) +
  ggtitle('sulphates X chlorides X quality')

p4 <- ggplot(data = wdf, aes(x = density, y = volatile.acidity, colour = quality)) +
  geom_point(alpha = 0.3) +
  geom_smooth(method='lm',formula=y~x) +
  scale_colour_gradientn(colours=rainbow(10)) +
  ggtitle('density X volatile.acidity X quality')


grid_multivariate <- grid.arrange(p1, p2, p3, p4, ncol = 2, top = textGrob("Multivariate Plots",gp=gpar(fontsize=15,font=3)))

ggsave(file = 'pictures/2_multivariate_outliers.png', grid_multivariate)
Multivariate scatter plot

Multivariate scatter plot

Multivariate Analysis

Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?

We can confirm the correlation between density and residual.sugar in the ggpairs plot and linear regression line over the previous one. I all of the 4 multivariate graphics we can observe a concentration for good wines instead normal and bad ones.

Machine Learning Models[#ml]

Creating Training and Test Datasets for Raw Data

# Loading wdf.raw dataset
wdf.raw <- read.csv('data/wineQualityWhites.csv')
wdf.raw$X <- NULL
wdf.raw$quality <- as.factor(wdf$quality)

# Creating train.raw and test.raw datasets
set.seed(13)
samp <- sample(nrow(wdf.raw), 0.4 * nrow(wdf.raw))
train.raw <- wdf.raw[samp, ]
test.raw <- wdf.raw[-samp, ]

Creating Training and Test Datasets for Outliers

# Loading wdf.outliers dataset
wdf.outliers <- data.frame(wdf.raw)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$fixed.acidity < 11)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$volatile.acidity < 0.75)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$citric.acid < 1)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$residual.sugar < 30)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$chlorides < 0.10)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$free.sulfur.dioxide < 125)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$total.sulfur.dioxide < 350)
wdf.outliers <- subset(wdf.outliers, wdf.outliers$density < 1.005)

# Creating Train.outliers and Test.outliers datasets
set.seed(13)
samp <- sample(nrow(wdf.outliers), 0.4 * nrow(wdf.outliers))
train.outliers <- wdf.outliers[samp, ]
test.outliers <- wdf.outliers[-samp, ]

Random Forest Model

# Random Forest Raw
df.list <- list(data.frame(train.raw), data.frame(test.raw))
a <- 0
while (a < 10){
  a <- a + 1
  model <- randomForest(quality ~ . - quality, data = train.raw)
  rf.pred <- predict(model, newdata = test.raw)
  acc.rf <- classAgreement(table(rf.pred, test.raw$quality))[1]
  time <- Sys.time() 
  str <- paste('rf', time, as.numeric(acc.rf), sep = ',')
  write(str, file = 'data/accuracy_models.csv', append = TRUE)
}

# Random Forest Raw
df.list <- list(data.frame(train.outliers), data.frame(test.outliers))
a <- 0
while (a < 10){
  a <- a + 1
  model <- randomForest(quality ~ . - quality, data = train.outliers)
  rf.pred <- predict(model, newdata = test.outliers)
  acc.rf <- classAgreement(table(rf.pred, test.outliers$quality))[1]
  time <- Sys.time() 
  str <- paste('rf.out', time, as.numeric(acc.rf), sep = ',')
  write(str, file = 'data/accuracy_models.csv', append = TRUE)
}

Tuning the parameters SVM

# Tune with raw dataset
obj.raw <- tune.svm(quality~., data = train.raw, gamma = 2^(-1:1),cost = 2^(2:4))
summary(obj.raw)
# tune with outliers dataset
obj.outliers <- tune.svm(quality~., data = train.outliers, gamma = 2^(-1:1),cost = 2^(2:4))
summary(obj.outliers)
SVM tune raw

SVM tune raw

SVM tune outliers

SVM tune outliers

Supported Vector Machines

# SVM raw
df.list <- list(data.frame(train.raw), data.frame(test.raw))
a <- 0
while (a < 10){
  a <- a + 1
  svm.model  <- svm(quality ~ ., data = train.raw, cost = 4, gamma = 0.5)
  svm.pred <- predict(svm.model,test.raw[,-12])
  acc.svm <- classAgreement(table(svm.pred, test.raw$quality))[1]
  time <- Sys.time() 
  str <- paste('svm', time, as.numeric(acc.svm), sep = ',')
  write(str, file = 'data/accuracy_models.csv', append = TRUE)
}

# SVM outliers
df.list <- list(data.frame(train.outliers), data.frame(test.outliers))
a <- 0
while (a < 10){
  a <- a + 1
  svm.model  <- svm(quality ~ ., data = train.outliers, cost = 4, gamma = 0.5)
  svm.pred <- predict(svm.model,test.outliers[,-12])
  acc.svm <- classAgreement(table(svm.pred, test.outliers$quality))[1]
  time <- Sys.time() 
  str <- paste('svm.out', time, as.numeric(acc.svm), sep = ',')
  write(str, file = 'data/accuracy_models.csv', append = TRUE)
}

Rpart

# rpart raw
df.list <- list(data.frame(train.raw), data.frame(test.raw))
a <- 0
while (a < 10){
  a <- a + 1
  rpart.model <- rpart(quality ~ ., data = train.raw)
  rpart.pred <- predict(rpart.model, test.raw[,-12], type = 'class')
  table(rpart.pred,test.raw[,12])
  classAgreement(table(pred = rpart.pred,true = test.raw[,12]))
  acc.rpart <- classAgreement(table(rpart.pred, test.raw$quality))[1]
  time <- Sys.time() 
  str <- paste('rpart', time, as.numeric(acc.rpart), sep = ',')
  write(str, file = 'data/accuracy_models.csv', append = TRUE)
}

# rpart outliers
df.list <- list(data.frame(train.outliers), data.frame(test.outliers))
a <- 0
while (a < 10){
  a <- a + 1
  rpart.model <- rpart(quality ~ ., data = train.outliers)
  rpart.pred <- predict(rpart.model, test.outliers[,-12], type = 'class')
  table(rpart.pred,test.outliers[,12])
  classAgreement(table(pred = rpart.pred,true = test.outliers[,12]))
  acc.rpart <- classAgreement(table(rpart.pred, test.outliers$quality))[1]
  time <- Sys.time() 
  str <- paste('rpart.out', time, as.numeric(acc.rpart), sep = ',')
  write(str, file = 'data/accuracy_models.csv', append = TRUE)
}

The Accuracy average for each Model

# load the dataset
acc.df <- read.csv(file = 'data/accuracy_models.csv')

# Random Forest
mean.acc.rf <- mean(subset(acc.df, acc.df$model == 'rf')$accuracy)
mean.acc.rf <- format(mean.acc.rf, digits = 4)
mean.acc.rf <- as.numeric(mean.acc.rf)*100

mean.acc.rf.out <- mean(subset(acc.df, acc.df$model == 'rf.out')$accuracy)
mean.acc.rf.out <- format(mean.acc.rf.out, digits = 4)
mean.acc.rf.out <- as.numeric(mean.acc.rf.out)*100

# SVM
mean.acc.svm <- mean(subset(acc.df, acc.df$model == 'svm')$accuracy)
mean.acc.svm <- format(mean.acc.svm, digits = 4)
mean.acc.svm <- as.numeric(mean.acc.svm)*100

mean.acc.svm.out <- mean(subset(acc.df, acc.df$model == 'svm.out')$accuracy)
mean.acc.svm.out <- format(mean.acc.svm.out, digits = 4)
mean.acc.svm.out <- as.numeric(mean.acc.svm.out)*100

# Rpart
mean.acc.rpart <- mean(subset(acc.df, acc.df$model == 'rpart')$accuracy)
mean.acc.rpart <- format(mean.acc.rpart, digits = 4)
mean.acc.rpart <- as.numeric(mean.acc.rpart)*100

mean.acc.rpart.out <- mean(subset(acc.df, acc.df$model == 'rpart.out')$accuracy)
mean.acc.rpart.out <- format(mean.acc.rpart.out, digits = 4)
mean.acc.rpart.out <- as.numeric(mean.acc.rpart.out)*100
htmlTable(acc.matrix,
          css.cell = ("padding-left: 1em; padding-right: 1em;"), 
          header =  c('Random Forest', 'SVM', 'Rpart'),
          rnames = c('RAW Data', 'Outliers Data'),
          caption="Accuracy Mean (%)")
## Error in htmlTable(acc.matrix, css.cell = ("padding-left: 1em; padding-right: 1em;"), : object 'acc.matrix' not found

Pricipal component analysis - PCA

To better understand how the features are correlated I ran a PCA algorithm and I did the plot for the PCA Components and a graphic with Variance x Number of Component to decide how many Components I will use in the following models.

# PCA
wdf.pca <- prcomp(wdf.outliers[,1:11], center = TRUE, scale. = TRUE)
# Variance plot
plot(wdf.pca, type = "l")
abline(h=0.55, v=8, col="blue")

# PCA components plots
g <- autoplot(wdf.pca, loadings = TRUE, loadings.colour = 'blue', loadings.label = TRUE, loadings.label.size = 5, alpha = 0.3, main = 'PCA')
ggsave(file = 'pictures/pca_outliers.png', g)
PCA Variance

PCA Variance

Looking at this graphic it is easy to indentify that we can run the models with 8 components without loosing accuracy in our model.

PCA components

PCA components

In this graphic we can confirm some teories about the correlation between the variables. For example we expect negative correlation with alcohol and residual.sugar once the alcohol needs sugar to be produced. pH and citric.acid and fixed.acidity also need to have negative correlation once the lowest pH means very acid solution.

New PCA Datasets

# New dataframe
new.wdf.pca <- data.frame(wdf.pca$x)
new.wdf.pca <- data.frame(new.wdf.pca[,1:8], quality = wdf.outliers$quality)

# Creating train and test datasets
set.seed(123)
samp <- sample(nrow(new.wdf.pca), 0.8 * nrow(new.wdf.pca))
new.train.pca <- new.wdf.pca[samp, ]
new.test.pca <- new.wdf.pca[-samp, ]

Random Forest Model after PCA

# Random Forest Raw
df.list <- list(data.frame(new.train.pca), data.frame(new.test.pca))
a <- 0
while (a < 10){
  a <- a + 1
  model <- randomForest(quality ~ . - quality, data = new.train.pca, ntree = 150)
  rf.pred <- predict(model, newdata = new.test.pca)
  acc.rf <- classAgreement(table(rf.pred, new.test.pca$quality))[1]
  time <- Sys.time() 
  str <- paste('rf', time, as.numeric(acc.rf), sep = ',')
  write(str, file = 'data/accuracy_models_pca.csv', append = TRUE)
}

Mean Random Forest Accuracy

# load the dataset
acc.df <- read.csv(file = 'data/accuracy_models_pca.csv')

# Random Forest
mean.acc.rf <- mean(subset(acc.df, acc.df$model == 'rf')$accuracy)
mean.acc.rf <- format(mean.acc.rf, digits = 4)
mean.acc.rf <- as.numeric(mean.acc.rf)*100
htmlTable(mean.acc.rf,
          css.cell = ("padding-left: 1em; padding-right: 1em;"), 
          header =  c('Random Forest'),
          rnames = c('Outliers Data'),
          caption="Accuracy Mean (%)")
Accuracy Mean (%)
Random Forest
Outliers Data 44.19

We could increase the accuracy in more than 4% with Random Forest and PCA.

Final Plots and Summary

Plot One

Description One

Plot Two

df.list <- list(data.frame(wdf), data.frame(wdf.outliers))
a <- 0
for (df in df.list){
  a <- a + 1
  d <- prcomp(df[,1:11], center = TRUE, scale. = TRUE)
  if (a == 1){
    g1 <- autoplot(d, loadings = TRUE, loadings.colour = 'blue', loadings.label =        TRUE, loadings.label.size = 5, alpha = 0.3, main = 'Raw')
  } else {
    g2 <- autoplot(d, loadings = TRUE, loadings.colour = 'blue', loadings.label =        TRUE, loadings.label.size = 5, alpha = 0.3, main = 'Outliers')  }
}

g.grid <- grid.arrange(g1, g2, ncol = 2,
  top = textGrob("Raw x Outliers PCA plot",gp=gpar(fontsize=15,font=3)))

ggsave(file = 'pictures/plot_two.png', g.grid)
Raw x Outliers PCA plot

Raw x Outliers PCA plot

Description Two

Plot Three

df.list <- list(data.frame(wdf), data.frame(wdf.outliers))
a <- 0
for (df in df.list){

  a <- a + 1
  
  p1 <- ggplot(data = df, aes(x = density, y = residual.sugar, colour = quality)) +
    geom_point(alpha = 0.3) +
    geom_smooth(method='lm',formula=y~x) +
    scale_colour_gradientn(colours=rainbow(10)) +
    ggtitle('density X residual.sugar X quality')


  p2 <- ggplot(data = df, aes(x = density, y = alcohol, colour = quality)) +
    geom_point(alpha = 0.3) +
    geom_smooth(method='lm',formula=y~x) +
    scale_colour_gradientn(colours=rainbow(10)) +
    ggtitle('density X alcohol X quality')


  p3 <- ggplot(data = df, aes(y = sulphates, x = chlorides, colour = quality)) +
    geom_point(alpha = 0.3) +
    geom_smooth(method='lm',formula=y~x) +
    scale_colour_gradientn(colours=rainbow(10)) +
    ggtitle('sulphates X chlorides X quality')


  p4 <- ggplot(data = df, aes(x = density, y = volatile.acidity, colour = quality)) +
    geom_point(alpha = 0.3) +
    geom_smooth(method='lm',formula=y~x) +
    scale_colour_gradientn(colours=rainbow(10)) +
    ggtitle('density X volatile.acidity X quality')

  if(a == 1){
     pm1 <- grid.arrange(p1, p2, p3, p4, ncol = 2, 
       top = textGrob("RAW",gp=gpar(fontsize=15,font=3)))
  } else {
     pm2 <- grid.arrange(p1, p2, p3, p4, ncol = 2, 
       top = textGrob("Outliers",gp=gpar(fontsize=15,font=3)))
  }
  
  file.name <- paste('pictures/', a, '_multivariate.png', sep = '')
  ggsave(file.name, grid_multivariate)
}

pm.grid <- grid.arrange(pm1, pm2, ncol = 2,
             top = textGrob("Multivariate Plots Raw data - Outliers data",
                            gp=gpar(fontsize=15,font=3)))

ggsave('pictures/plot_three.png', pm.grid)
Raw and Outliers Multiplot

Raw and Outliers Multiplot

Description Three

Reflection

The models I made didn’t perform as well as I expected. The accuracy with PCA was a good choice to try to eliminate useless information in the dataset and we could see in the results some accuracy improvement. Removing the outliers we got a better result with and without PCA of around 3%.

General resources

Articles

  • Modeling wine preferences by data mining from physicochemical properties by Paulo Cortez,Ant?nio Cerdeira, Fernando Almeida, Telmo Matos, Jos? Reis. (2009) 547-553
  • Support Vector Machines, The Interface to libsvm in package e1071 by David Meyer
  • A Practical Guide to Support Vector Classification by Chih-Wei Hsu, Chih-Chung Chang, and Chih-Jen Lin (2016)